On a Discrete Version of the Mohr-Mascheroni Theorem

Marius Munteanu, Laura Munteanu

Department of Mathematics, Computer Science, and Statistics, State University of New York, College at Oneonta, USA.

DOI: 10.4236/am.2013.411A4002                

Abstract

We introduce a new geometric tool called n-compass and show that the famous theorem of Mascheroni and Mohr remains valid if the traditional compass is replaced by the newly introduced tool.

Keywords

Mohr-Mascheroni Theorem; n-Compass

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. Mascheroni, “Geometrie du Compas,” Monom, 1980.
[2]	G. Mohr, “Euclides Danicus,” Copenhagen, 1928.
[3]	N. Hungerbuhler, “A Short Elementary Proof of the Mohr-Mascheroni Theorem,” American Mathematical Monthly, Vol. 101, No. 8, 1994, pp. 784-797. http://dx.doi.org/10.2307/2974536
[4]	A. Avron, “Theorems on Strong Constructibility with a Compass Alone,” Journal of Geometry, Vol. 30, No. 1, 1987, pp. 28-35. http://dx.doi.org/10.1007/BF01223260
[5]	A. Avron, “On Strict Strong Constructibility with a Compass Alone,” Journal of Geometry, Vol. 38, No. 1-2, 1990, pp. 12-15. http://dx.doi.org/10.1007/BF01222890
[6]	V. Pambuccian, “Axiomatizing Geometric Constructions,” Journal of Applied Logic, Vol. 6, No. 1, 2008, pp. 24-46. http://dx.doi.org/10.1016/j.jal.2007.02.001
[7]	Z. Zhang, L. Yang and X. R. Hou, “What Can We Do with Only a Pair of Rusty Compasses?” Geometriae Dedicata, Vol. 38, 1991, pp. 137-150. http://dx.doi.org/10.1007/BF00181213
[8]	V. J. Baston and F. A. Bostok, “On the Impossibility of Ruler-Only Constructions,” Proceedings of the American Mathematical Society, Vol. 110, No. 4, 1990, pp. 10171025. http://dx.doi.org/10.1090/S0002-9939-1990-1034882-3
[9]	D. Fog, “Om Konstruktion Med Passeren Alene,” Mathematisk Tidsskrift A, 1935, pp. 16-24.
[10]	V. S. Martynenko, “Mascheroni’s Theorem in Lobachevski Geometry,” Doklady Akademii Nauk Ukrainskoj SSR, Ser A, Vol. 1, 1982, pp. 22-27.